View of /trunk/NationalProblemLibrary/ASU-topics/setTrigGraphs/p9.pg

    1 ## DESCRIPTION
    2 ## Precalculus: Trigonometry
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('precalculus','trigonometric graphs')
    6 ## Tagged by cmd6a 6/21/06
    7 
    8 ## DBsubject('Trigonometry')
    9 ## DBchapter('Trigonometry Functions of Real Numbers')
   10 ## DBsection('Trigonometric Graphs')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('ASU')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 
   20 DOCUMENT();        # This should be the first executable line in the problem.
   21 
   22 loadMacros(
   23 "PG.pl",
   24 "PGbasicmacros.pl",
   25 "PGchoicemacros.pl",
   26 "PGanswermacros.pl",
   27 "PGauxiliaryFunctions.pl",
   28 "PGgraphmacros.pl",
   29 "PGasu.pl"
   30 );
   31 
   32 TEXT(beginproblem());
   33 
   34 
   35 $a=random(-4, -1);
   36 $c=random(3,7,2);
   37 
   38 $b=1/$c;
   39 $h_shift=random(1,$c-1);
   40 
   41 $x1dom=2*$c+$h_shift;
   42 $x2dom=2*$c-$h_shift;
   43 $ydom=abs($a)+1;
   44 $xgrid=$x1dom+$x2dom;
   45 $ygrid=2*$ydom;
   46 
   47 $graph = init_graph(-$x1dom,-$ydom,$x2dom,$ydom,'axes'=>[0,0],'grid'=>[$xgrid,$ygrid]);
   48 $f = FEQ("$a*cos((pi/$c)*(x-$h_shift)) for x in <-$x1dom,$x2dom> using color:blue and weight:2");
   49 ($fref) = plot_functions( $graph, $f);
   50 $period = 2*$c;
   51 
   52 # Label some points
   53 #$label1 = new Label(0,$a, "$a",'black','right');
   54 #$label2 = new Label($period, 0, "($period,0)",'black','left');
   55 #$d = -$a;
   56 #$label3 = new Label(0,$d,"$d",'black','right');
   57 #$graph->lb($label1, $label2, $label3);
   58 
   59 $val=$h_shift-$period;
   60 
   61 BEGIN_TEXT
   62 \{ image(insertGraph($graph)) \} $PAR
   63 To get a better look at the graph, you can click on it.
   64 $PAR
   65 The curve above is the graph of a sinusoidal function.  It goes through
   66 the points \( ($val,$a) \) and \( ($h_shift,$a) \).
   67 Find a sinusoidal function that matches the given graph. If needed, you can enter
   68 \(\pi\)=3.1416...  as 'pi' in your answer, otherwise use at least 3 decimal digits.
   69 $PAR
   70     \(f(x) = \) \{ans_rule(60)\}
   71 END_TEXT
   72 
   73 $ans = "$a*cos((pi/$c)*(x-$h_shift))";
   74 
   75 ANS(fun_cmp($ans, limits=>[-$x1dom,$x2dom], vars=>"x"));
   76 
   77 ENDDOCUMENT();        # This should be the last executable line in the problem.